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МатематикаРешебник по алгебре 8 класс Мерзляк Задание 732
Задание 732
\[\boxed{\mathbf{732\ (732).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[x^{2} + 5x - 16 = 0\]
\[x_{1} + x_{2} = - 5;\ \ \ \ x_{1} \cdot x_{2} = - 16\]
\[1)\text{\ x}_{1}²x_{2} + x_{1}x_{2}² =\]
\[= x_{1}\left( x_{1}x_{2} + x_{2}^{2} \right) =\]
\[= x_{1}x_{2}\left( x_{1}{+ x}_{2} \right) = - 16 \cdot ( - 5) =\]
\[= 80\]
\[2)\ \frac{x_{2}}{x_{1}} + \frac{x_{1}}{x_{2}} = \frac{x_{2}^{2} + x_{1}^{2}}{x_{1}x_{2}} =\]
\[= \frac{x_{2}^{2} + x_{1}^{2} + 2x_{1}x_{2} - 2x_{1}x_{2}}{x_{1}x_{2}} =\]
\[= \frac{\left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2}}{x_{1}x_{2}} =\]
\[= \frac{25 + 32}{- 16} = - \frac{57}{16} = - 3\frac{9}{16}\]
\[3)\ \left| x_{2} - x_{1} \right| = \sqrt{\left( x_{2} - x_{1} \right)^{2}} =\]
\[= \sqrt{\left( x_{2}^{2} + x_{1}^{2} - 2x_{1}x_{2} \right)} =\]
\[= \sqrt{\left( x_{1} + x_{2} \right)^{2} - 4x_{1}x_{2}} =\]
\[= \sqrt{25 - 4 \cdot ( - 16)} = \sqrt{89}\ \]
